Chen Han, Gao Guangjian, Hu Ning, Deng Mingxi, Xiang Yanxun
Department of Physics, Army Logistics University, Chongqing 401331, China.
College of Aerospace Engineering, Chongqing University, Chongqing 400044, China.
Ultrasonics. 2020 May;104:106109. doi: 10.1016/j.ultras.2020.106109. Epub 2020 Feb 24.
This work investigates modeling of the frequency mixing response (FMR) induced by two counter-propagating Lamb waves with different frequencies in a two-layered plate, and then numerically simulates and analyzes the influences of interfacial properties on the effect of FMR. Based on a perturbation approach and a normal-mode-expansion technique for waveguide excitation, the second-order bulk driving forces and surface/interface stresses at the mixing frequency, originated from the interaction of two counter-propagating Lamb waves within the wave mixing zone, can be regarded as the excitation sources for generation of a series of combined harmonics. It is found that, under the internal resonance condition including the phase matching and nonzero energy flux, the magnitude of the combined harmonic generated increases with increase in the length of mixing zone of the two counter-propagating Lamb waves, and tends to be stable outside the wave mixing zone. Due to the relatively short mixing zone of the two counter-propagating Lamb waves, the effect of FMR has attracted considerable attention because it can enhance the accuracy of location of the local interfacial degradation in the given layered plate. Both the numerical analyses and finite element (FE) simulations performed show that the local interfacial degradation in the two-layered plate may be assessed and located by spatial scanning of wave mixing zone of the two counter-propagating Lamb waves. Through modeling and FE simulations, this paper provides an insight into the physical process of FMR of the two counter-propagating Lamb waves in a two-layered plate, and meanwhile shows a potential for assessment and location of the local interfacial degradation by using the effect of FMR of the two counter-propagating Lamb waves.
本文研究了两层板中两个不同频率的反向传播兰姆波引起的频率混合响应（FMR）建模，然后对界面特性对FMR效应的影响进行了数值模拟和分析。基于微扰法和波导激励的简正模展开技术，在波混合区内两个反向传播兰姆波相互作用产生的混合频率下的二阶体驱动力和表面/界面应力，可视为产生一系列组合谐波的激励源。研究发现，在内共振条件下，包括相位匹配和非零能量通量，产生的组合谐波的幅值随着两个反向传播兰姆波混合区长度的增加而增大，并且在波混合区外趋于稳定。由于两个反向传播兰姆波的混合区相对较短，FMR效应因其能提高给定层板中局部界面退化位置的精度而备受关注。所进行的数值分析和有限元（FE）模拟均表明，两层板中的局部界面退化可通过两个反向传播兰姆波的波混合区的空间扫描来评估和定位。通过建模和FE模拟，本文深入了解了两层板中两个反向传播兰姆波FMR的物理过程，同时展示了利用两个反向传播兰姆波的FMR效应评估和定位局部界面退化的潜力。
